Question

a plane which passes through the point (3,2,0) and the line x-4/1=y-7/5=z-4/4 is

Answer 1

Answer:

Infinite Planes

Step-by-step explanation:

Hi,

Given point (3, 2, 0) lies on the given line x-4/1=y-7/5=z-4/4,

hence there would be infinite planes passing through the given line. Some

more information is needed to find a equation of the unique plane passing

through the given plane.

If the given question was  a Multiple Choice Question, then check out each

option satisfying the given points (3, 2, 0) or any other point on the given

line say (4 , 7, 4) or any point of the form ( 4 + t, 7 + 5t, 4 + 4t).

Hope, it helped !

Answer 2

Solution:

Standard equation of a plane passing through a point is given by

$a(x - x1) + b(y - y1) + c(z - z1) + d = 0$
here point is (3,2,0)

$a(x - 3) + b(y - 2) + c(z - 0) + d = 0$
Since the plane passing through the line

$\frac{x - 4}{1} = \frac{y - 7}{5} = \frac{z - 4}{4}$
here Direction ratio of line are (1,5,4)

and point lie on the line are (4,7,4)

Hence plane's normal is perpendicular to the line

$a(4 - 3) + b(7 - 2) + c(4 - 0) = 0 \\ \\ a + 5b + 4c = 0 \\ ..eq1$
and
$a + 5b + 4c = 0...eq2$
eq 1 and 2 are same,thus both the equation meets at infinite points,Thus there are such infinite planes,which passes through the given point and parallel to the given line.

Hope it helps you.